The ¬nal equation describing the FMV is:11

n k k1

FMV (VC) P(i i 1) [1 P(VCj/j)]

k1 i1 j0

P(VCk k) SH%k $100 million (12-5)

In words, the contribution to FMV from the VC scenario is the sum of

the probabilities of obtaining VC, which we quanti¬ed in equation

(12-4), times the $100 million FMV of the company, assuming it is VC

¬nanced.

Section 1B: The Bootstrap Scenario Assuming Debt

Restructuring with Parent

Bootstrapping occurs when the Company fails to attract venture capital

but still manages to stay in business. The bootstrap scenario includes both

success and failure at its attempts to bootstrap. Figure 12-2 shows the

decision tree for the bootstrap scenario.

The pattern of events is that in each iteration, the Company can make

the sale or not make the sale. After each sale, it might get VC ¬nancing

or it might not. In section 1B we are not interested in the nodes on the

decision tree where the Company receives VC ¬nancing, as we have al-

ready quanti¬ed that in section 1A. Thus, we do not show those nodes.

Nevertheless, it is important to account for the probabilities of obtaining

VC ¬nancing because if we don™t, we will be double-counting that portion

of the time that the Company could ¬nance through a VC or bootstrap

successfully. The Company can™t do both at the same time. Thus, we

remove the statistical probability of overlap. We accomplish that by mul-

tiplying all probabilities by [1 P(VCi i)] for all relevant i, where i is the

sale number (also the iteration number).

If the Company does not make the sale, then it has a probability of

survival and failure. We denote the survival after its last sale as Sj, where

j is the sale number. The conditional probability of survival after its last

sale is P[Sj j, ( j 1)]. For example, if the company makes sale #3, does

not make sale #4, and survives, we denote that as S3, and its conditional

11

The term SH% is the percentage ownership of the current shareholders after VC ¬nancing.

PART 5 Special Topics

424

F I G U R E 12-2

Decision Tree for Bootstrapping Assuming Debt Restructure and No Venture Capital

P(-VC4|4)(0.9)

Survive = S4

Make Sale 4

P(-VC3|3)(0.8)

No VC3

Fail

Sale 3 Sale 3

Make

P(-VC2|2)(0.6) 0.75

No Sale 4 Survive = S3

No VC2

No VC3

P(-VC3|3)(0.2)

Fail

0.25

P(-VC1|1)(0.9) Make Sale 2 0.35

No Sale 3 Survive = S2

No VC1

No VC2

P(-VC2|2)(0.4)

Fail

0.65

0.3

No Sale 2 Survive = S1

Make Sale 1

P(1)=0.75

No VC1

P(-VC1|1)(0.1)

START Fail

0.7

No Sale 1

Fail

P(-1)=0.25

Note: P(-VC1|1) is equivalent to [1-P(VC1|1)] in the text.

probability of occurrence is P(S3 3, 4), which reads, ˜˜the probability of

Company long-term survival, given that it made sale #3, but does not

make sale #4.™™ If the Company makes the next sale, then we repeat the

iteration, incrementing the sale number.

Without going through all of the step-by-step analysis we did for the

VC scenario, the FMV of the bootstrap scenario is:

j

n

FMV (Bootstrap) P(i i 1)[1 P(VCi i)]

(12-6)

j1 i1

(1 P( j 1 j)P[Sj j, (j 1)]FMV (Sj)

Let™s use the ¬rst iteration as an example. The probability of making

sale #1 is 0.75. There is a 0.5 probability of obtaining VC ¬nancing if the

company makes sale #1, so there is also a 0.5 probability of not obtaining

VC ¬nancing, i.e., [1 P(VCi i)] 0.5. In order to terminate at S1, the

company must make sale #1 and fail to make sale #2, which means we

multiply by [1 P(2 1)], which is equal to one minus the conditional

probability of making sale #2 1 0.9 (B30) 0.1. The probability of

survival if the Company makes sale #1 but stops there is 0.30 (G29). Thus,

P(S1) P(1) [1 P(VC1 1)] [1 P(2 1)] P(S1 1, 2) 0.75 (1

12

0.5) (1 0.9) 0.3 1.125% (H29).

Column I is the conditional FMV of the company at each respective

event level. This is different than in section 1, where the FMV is the same

12

Note that for the last milestone, 1 P(n 1 n) must be equal to 1, since the probability of

making the (n 1)st sale is zero.

CHAPTER 12 Valuing Startups 425

regardless of stage. The reason is that in section 1 the sole objective is

obtaining venture capital funding, which will enable the Company to sell

to the world. The lost pro¬ts on the key sales not made is immaterial

compared to the $100 million FMV. In contrast, in section 1B each sale is

signi¬cant relative to the total value and adds to the value of the com-

pany.13

In section 1B we begin with a conditional FMV of $16,000,000 (B44,

repeated in I32). That value contains an implicit assumption that the

Company makes it to event #4, the sale to Company #4. At each level

before that, we subtract the net present value of the after-tax pro¬ts14 from

the sale that does not occur, i.e., we work our way backwards up this

column. We assume pretax pro¬ts of $750,000 for the sales in events #3

and #4 and $500,000 for event #2. The numbers are then tax effected and

discounted to present value. If the Company does not make it to event

#1, this model assumes the Company fails entirely and has a zero value.

Column J is the contribution to the FMV of the Company on a control

basis coming from the bootstrap scenario and is simply column H times

column I, which totals $521,603 (J33).

Column K is the same value as column J, except that it is a minority

interest conditional FMV. The discount for minority interest is 25%, which

appears in B45. On a minority interest basis, the bootstrap scenario FMV

is $391,202 (K33).

Section 2: No Restructure Scenario

The ¬nal scenario is the no-restructure with parent scenario. Section 2 is

identical to section 1B, except:

1. Column F, the probability of not obtaining venture capital

¬nancing, is 100% by de¬nition for all four events in section 2,

since the president informs us that a VC will not ¬nance the

Company as long as it still has the parent™s debt on the books.

2. Column I is calculated identically to section 1B, except that the

baseline FMV as calculated by DCF analysis is $8 million (C44,

repeated in I40) for the no-restructure scenario instead of $16

million (B44, repeated in I32).

Columns J and K in section 2B are the same as in Section 2A, except

that there are no values originating from the venture capital scenario that

have to be removed.

Section 3: FMVs per Share under Various Restructure

Scenarios

In section 3 we calculate the fully diluted FMV per share post-transaction

under the various scenarios.

13

The sales actually do affect the values in section 1, but their impact is immaterial relative to the

much larger total value, which is not true in the bootstrap scenarios.

14

To be more precise, we would also include the related cash ¬‚ow effects.

PART 5 Special Topics

426

Venture Capital Scenario. The conditional FMV of the Company on

a minority interest basis from the venture capital scenario is $27,391,050

(B53, transferred from J15). The Company currently has 1,000,000 shares

of common stock outstanding, as appears in B55, C55, and F55. Rows 57“

59 show employee stock options. Row 57 shows outstanding options for

200,000 shares at $0.50 per share. These options are in the money, and we

assume they will be exercised. That would result in $100,000 being paid

to the Company, which is included in the DCF analysis and is therefore

already incorporated into the $27,391,050 value. These 200,000 additional

shares are taken into account in all of the valuation scenarios.

Rows 58 and 59, however, are for options that are granted but could

only be exercised if the Company does the restructure and obtains VC

¬nancing.15 Mr. Johnson says that if the Company does obtain VC ¬-

nancing, it will issue 66,667 options with a $0.75 exercise price this year

(B58) and 100,000 options (B59) at a $1.00 per share exercise price next

year. Again, the cash in¬‚ows from exercise of the options are already

included in the DCF analysis.

In the restructure scenario the parent receives $400,000 of preferred

stock, which can be converted to common if the Company goes public or

gets acquired. Otherwise, it only serves to increase the liquidation pref-

erence, as preferred dividends will never be paid. Therefore, the divi-

dends, which are not tax deductible, do not appear in any of the cash

¬‚ows. We presume in the venture capital scenario that the probability of

going public or being acquired is signi¬cant and that preferred will con-

vert. According to Mr. Johnson, a reasonable conversion ratio is 4 to 1. In

note 3 to section 3 the $400,000 is divided by four times the fully diluted

FMV of $10.391 per share (D66, repeated in footnote [3]) or $41.56 per

share, resulting in an estimated conversion to common shares of 9,624

(footnote [3], transferred to B60). This calculation is a simultaneous equa-

tion and requires the use of multiple iterations on the spreadsheet. The

number of converted shares depends on the fair market value per com-

mon share, but the FMV per common share depends on the number of

preferred shares.

The total option shares are 376,290 (B61), including the assumed con-

version of preferred in the venture capital scenario. In B63 we show the

proposed issuance of 1.3 million shares to the president. Adding the

1,000,000 original shares, 376,290 option granted shares, and the 1.3 mil-

lion new shares, we come to 2,676,290 (B65) fully diluted shares in the

venture capital scenario. Dividing the $27,391,050 FMV by 2,676,290

shares, we arrive at the FMV per share of $10.235 (B66) for the venture

capital scenario.

Next we consider the bootstrap portion of the restructure scenario.

We begin with the $391,202 (K33) FMV as calculated in section 1B and

repeat it in C53. Again, this is the portion of bootstrap value from which

venture capital is excluded.

In this scenario the fully diluted shares are the same as in the venture

capital scenario, except that the 66,667, 100,000 and 9,624 shares in rows

15

The Company cannot obtain VC ¬nancing without restructuring its debt.

CHAPTER 12 Valuing Startups 427

58“60 are zero in this case. There are 1,200,000 shares (C62) in this sce-

nario before issuing the 1.3 million, and 2,500,000 (C65) shares after doing

so. Dividing $391,202 by 2,500,000 shares, we come to a FMV of this

scenario of $0.156 (C66) per share. Adding the per share values together,

we come to $10.235 $0.156 $10.391 (B66 C66 D66) as the

weighted average conditional FMV of the restructure scenario.

No-Restructure Scenario. The name of this scenario is somewhat of

a misnomer. It means that the Company does not restructure its debt with

the parent. At the onset of this assignment there was no way to know

this, but restructuring of debt would eventually be required. The dis-

counted cash ¬‚ow analysis leads to the conclusion that the Company is

unlikely to be able to generate enough cash to pay off the parent™s note

by its due date of December 31, 200016 ”even though the forecast shows

pro¬ts. Therefore, the Company has two choices: become insolvent and

undergo liquidation or restructure later, and undergo a distress sale of

equity approximately one year before the note becomes due.

The second choice obviously leads to a higher value for the share-

holders, as it preserves the cash ¬‚ows, even though some of them will

be diverted to the new investor. Accordingly, we ran a DCF analysis to

the ¬scal year ending closest to the due date of the note. That value is

$8,000,000 and appears in C44.

The subtotal number of shares is 1,200,000 (F62) before the new in-